Equatorially trapped waves in a background meridional shear

The equatorial atmosphere harbors a large spectrum of waves that are trapped near and travel along the equator. These equatorially trapped waves interact nonlinearly with each other and with the planetary-barotropic waves.

Here, we consider advected shallow water equations that represent interactions of these equatorial waves with a prescribed meridional-barotropic shear. We show that in the presence of an easterly shear, the eigenfrequencies of westward propagating waves decrease compared to their free analogues. The effect is more significant for larger wavenumbers. However, for most eastward going waves with high wavenumbers, the eigenfrequencies increase compare to the shear-free case.

We emphasize the case of Kelvin waves, which are believed to play a central role in organized tropical convective systems. We demonstrate that unlike their free analogues that have no meridional velocity, the shear-forced Kelvin waves exhibit a weak meridional velocity, which, nevertheless, induces a large contribution to the flow convergence as observed in nature. Low-level convergence of moisture is believed to play a central role in sustaining moist convection in tropical convective systems.

In addition, the shear-Kelvin wave interaction excites three other equatorial waves: a Rossby wave, eastward and westward Gravity waves of weaker strength but their phase speeds and wave structures despite some quantitative differences, resemble those of the dry waves. We show that the effect of the shear is more significant for larger wavenumbers and/or stronger shears.

Furthermore, we look at the interactions between the meridional shear and other equatorial waves. We show that the shear makes the westward Yannai wave and some Rossby waves instable and interestingly the stable Rossby waves move eastward rather than westward. We demonstrate that in the sheared environment some waves are more/less trapped near the equator than their free counterparts. This can significantly modify the way in which the equatorial waves interact with the extratropical waves, i.e. the tropical-extratropical interactions and teleconnection patterns of weather and climate.